# -*- coding: utf-8 -*-

"""
created by huash06 at 2015-07-07 16:26

Given an array of integers, find out whether there are two distinct indices i and j in the array such
that the difference between nums[i] and nums[j] is at most t and the difference between i and j is at most k.

"""
__author__ = 'huash06'

import datetime
import sys
import math
import collections


class Solution:
    # @param {integer[]} nums
    # @param {integer} k
    # @param {integer} t
    # @return {boolean}
    def containsNearbyAlmostDuplicate(self, nums, k, t):
        if not nums:
            return False

        if t == 0:
            return len(nums) != len(set(nums))

        if k <= 0:
            return False

        if k >= len(nums):
            nums = sorted(nums)
            for i in range(len(nums) - 1):
                if abs(nums[i] - nums[i + 1]) <= t:
                    return True
        else:
            # 折半查找
            oms = sorted(nums[:k + 1])
            for i in range(k):
                if abs(oms[i] - oms[i + 1]) <= t:
                    return True

            i = 0
            for j in range(k + 1, len(nums)):
                oms.remove(nums[i])
                i += 1

                l = self.bsect(oms, nums[j])
                if l > 0 and abs(oms[l - 1] - nums[j]) <= t:
                    return True
                if l < len(oms) and abs(oms[l] - nums[j]) <= t:
                    return True
                oms = oms[:l] + [nums[j]] + oms[l:]
        return False

    def bsect(self, nums, val):
        left = 0
        right = len(nums)
        while left < right:
            mid = left + (right - left) // 2
            if nums[mid] == val:
                return mid
            elif nums[mid] < val:
                left = mid + 1
            else:
                right = mid
        return right


s = Solution()
print(s.containsNearbyAlmostDuplicate([1, 2], 0, 1))
print(s.containsNearbyAlmostDuplicate([2, 1], 1, 1))
print(s.containsNearbyAlmostDuplicate([-1, -1], 1, -1))
startTime = datetime.datetime.now()
s.containsNearbyAlmostDuplicate(
    [2433, 3054, 9952, 6470, 2509, 8502, -8802, -5276, 6559, -9555, -4765, 6399, 6543, 2027, 1723, -3032, -3319, -7726,
     -1425, -7431, -7492, 4803, 7952, -6603, -784, -8011, 6161, -6955, 5800, 5834, -6310, 1097, 2327, -4007, 8664,
     -9619, 5922, 518, 9740, 9976, 4257, -7803, 6023, 4189, -5167, -4699, 2441, 5941, 3663, 625, 5402, -3447, 8888,
     9040, -4811, -7547, 6822, 1415, 9372, -9262, 4584, 4149, -276, -4019, 198, 608, -4466, 5383, 7871, 3149, -8358,
     9270, 3565, -882, -9494, -6475, 9833, -7744, -598, 5299, 5976, 7361, -9444, 3771, -5718, 9051, 3469, -4028, 4216,
     5506, -8611, -9744, -8007, 213, -3454, -2420, 6283, -5616, -3508, -1329, 4694, -7219, 2056, 9063, -9648, -7722,
     -755, -9482, 9078, -8411, -3393, -4395, -1203, -2165, 2170, 8643, -5205, 4050, -9322, 6178, -973, -331, 7559,
     -7889, 3499, -7195, 7725, -9155, 3899, -5259, 1981, 4766, 595, -7183, 4150, -2062, 3288, 5047, -9789, 1507, -4937,
     5909, -3442, -4599, -789, 6931, -3100, -9151, -3665, -4228, -7466, 6393, 6632, -5133, -7684, 4525, 1150, 3826,
     -6424, -1689, 6206, -5747, 8061, 1502, -3893, -8528, 2387, -6159, -1355, -5789, 1361, -1593, -8955, 4505, 8885,
     -7793, 8038, -8401, 9688, 6241, 2518, 7115, -7193, -2735, 5665, 8331, -1822, -6938, 3307, 4019, 6020, -8340, -7138,
     4478, -6911, -1241, 3829, -5387, -3139, -1707, -187, -9148, -8734, -9570, 4666, -9280, -31, -4474, -5569, 548,
     5768, -7954, -9796, 9525, -56, -450, -7316, 5987, 25, -9590, 586, -4942, -8193, -3165, 6832, 1436, -106, -7393,
     -6921, -9176, 8404, 1220, 9014, 224, 2145, 4099, -3517, -6904, 6707, 3274, 1374, 1868, -2740, -3041, -9858, 6342,
     -166, -3181, 6941, 1132, -685, -8060, -7796, 5228, 9936, -15, -8382, -76, 4910, -9735, -8025, 9225, -4619, 4279,
     5578, 1910, -659, 834, 1501, 7328, -8782, -6110, -4776, 1321, 5721, 2014, 5767, -5541, -7052, -2716, 7768, -5243,
     -5997, 7162, 3157, -8769, 2776, 3018, 6159, 7571, -3806, -6260, -3565, 5508, 6517, -9469, 9652, 4320, 8409, 7357,
     3609, 4760, 1162, -1186, -6994, -2294, 1820, -3094, -9049, -2426, 9577, 7051, -8080, -4335, 3428, 4351, 1729, 9169,
     989, 1624, -1275, -577, 5765, -7344, -8206, -4561, 8191, 1709, 4416, 9256, 2439, 3907, -696, 4164, -5627, 3748,
     -1003, -7352, -9282, 4822, -877, -5078, 2783, -8127, 8810, -5625, -3563, -3644, 4009, -3791, -5544, 3696, -7041,
     -6941, -54, -2702, -8501, 4985, 7330, 7466, 526, -2886, 8098, -2973, -6142, -8740, -2965, -2264, -8868, -5292,
     -7997, 8192, -4444, -1954, 1634, 8758, -6569, -5179, -6504, -8153, 1787, 8669, -8513, -9875, 1694, 3144, -9540,
     -2051, -927, 2037, 1708, -1464, -9667, 6297, 7912, -1327, 785, -3514, 9784, 1840, 3709, -5542, -4282, -8051, 7006,
     -3899, 9159, 9430, 7492, -2751, -5174, 5860, 1499, -9942, -4468, -5941, 5589, -5699, 5429, 6743, 8444, -2039,
     -6824, -1257, -5906, 8266, -3831, 5392, 1645, 320, 1572, -9595, -454, 7877, -8070, -8432, -7719, -4199, 6043,
     -5002, 7800, 2363, -2493, 2626, 3390, 6243, -2734, 7055, 8290, 5547, 2828, -4021, 3943, -5139, 8892, 1597, -7757,
     7532, -3109, 8516, 8161, -8882, -3209, 6165, 7309, -1325, 7792, 7918, -3936, 7859, -7681, -4647, -6123, 2293,
     -9438, -5270, -5978, -4520, -9347, -4569, 7858, 8471, 910, -6564, -9980, -1603, -7042, 5674, 2103, -9855, -9269,
     5549, -4239, 4236, 8890, 9624, 1528, 9666, 3458, -643, -6591, -9008, -6535, -5993, -2978, -3478, -4844, 3370, 2072,
     -5256, -8584, -7659, 4674, -2893, -7729, -2212, 2792, -9012, 5011, 5325, 1698, 9680, 894, -8603, 4059, -4729,
     -8749, -3854, 2875, -527, -9600, 3236, -6607, -4491, -3488, -1586, -1579, -9039, -372, -2798, 8904, 1688, -1669,
     -83, -8200, -490, -6849, 9792, 90, -9453, 9725, -3525, -221, 5067, 4441, 796, 5324, 5284, 8709, -5893, 8174, 970,
     -1067, -9517, 2046, 1590, -2975, 9544, -7984, -7701, 8644, 8456, -212, 77, 5664, -7414, 8321, 7407, -756, 7649,
     -4851, -1071, 278, -5076, 6462, -8670, -4849, 914, -4500, 5401, -7112, -4464, -7643, -3685, -5307, 1749, 6949,
     1478, -6243, 9320, 2516, -798, 9095, 5627, 6327, -185, -6435, 8979, 6985, 4570, 6442, -909, 3919, 1880, 4593,
     -2440, 2523, 7331, 2662, 4287, 3712, 4071, -2609, -9451, -6762, -5388, -1929, 8572, 3566, 1354, 1957, -147, -1628,
     6002, -4368, 8312, -2033, -6340, -4190, -8975, 6894, 177, -3761, 2310, 3794, -8940, 1444, -6522, 325, -1908, -88,
     -3091, -7472, 5990, -5134, 8089, -9055, -9485, 2582, -6927, 5660, -3187, 8264, 8960, -1842, 3308, -1809, -1378,
     2943, 430, 2192, 364, -9458, 1143, 8672, 4037, -7739, 9640, -2534, -272, -3122, 417, 693, -2732, -7286, 8564,
     -8604, 850, -1055, 9967, -7016, -3601, -1125, -7953, 5331, 2822, 2729, -3483, 1048, -8439, 9281, 2960, 1539, 4929,
     -5151, 2635, -7023, -8865, -567, -3486, -6882, -1892, 3741, 5260, -7132, -453, 6482, 1433, -8227, 2897, 6354, 686,
     -9429, -9521, -6943, -329, -4735, 7590, -6850, 8844, 5423, 3169, -2041, 7308, 7823, -7166, 6927, -1738, -1644,
     -7447, 1238, -9832, -7865, -6837, -7097, 9469, -1927, -7043, 6872, -2683, -5509, 7301, 5147, -3235, 5039, -4323,
     6414, 1104, 4745, -6222, 4113, -6663, -5571, 7765, 7034, 7741, -2855, -7126, 5866, -5831, 2790, 9748, 8665, -2383,
     761, -690, 4540, 7229, -8187, 10, 6426, -6312, 8287, -8522, -4186, 2083, 8592, 3843, 8052, -9844, 8562, 671, 1969,
     4215, 2178, 1686, -9412, -5527, -1193, 6643, -5515, -5389, 3820, -7104, 9546, 1409, 6613, 1086, -3375, 1192, -382,
     6891, -4693, -8897, 763, 3457, 2538, -2011, -9687, 5935, 8929, 7525, 3583, -8451, 792, -5564, 7589, 9828, -488,
     4846, -268, 5675, -1462, 8345, 2868, -2189, -509, -6179, -1624, 1404, 8326, -5867, 2224, -5598, 2684, 5628, 5000,
     5586, -5596, 104, -2182, -5108, -3698, 5107, -8532, 5697, 6932, -6650, 6223, 1950, -7535, 2515, -1153, 2927, 6450,
     -9417, -668, -2708, -5852, 7896, 4219, -6388, 6457, 8170, 9459, -1415, 2075, -672, 7471, 6784, 909, 3362, 2855,
     -7060, 276, 2460, 214, -28, 3590, 5360, -1444, -6224, 5706, 5787, -650, -9022, 3981, -9607, -8154, -186, -326,
     -7585, 758, 5317, -4695, 8878, 3850, 8796, 7252, -2816, 158, -6765, 5338, 848, -7147, 7581, -7842, 3101, 2660,
     -6171, 9011, -6455, 567, -8751, 8970, 6860, 9899, -1916, -379, 9836, 9812, 5918, 4767, -6087, -6304, -3743, -8908,
     -870, -7500, 3316, 655, 6576, -4136, 2322, 8475, 678, 4156, -7231, 4017, -2007, 3045, 5605, 6209, 3656, 3533, 3176,
     1190, 9311, -6433, 2446, 2022, 2546, -2880, -9502, -3760, 5612, 8343, -3062, 9484, 3510, -7716, 4638, 8716, 5799,
     -7091, 7261, 4651, -2252, 8911, -2245, -8361, 6840, 8027, -7820, -674, -5250, 916, 935, 9579, 7335, -3061, 47,
     -1549, 1268, 3737, -3646, -6254, -9574, -3325, -944, -328, -7886, 174, 8521, 2926, -984, 6098, 5908, -2587, 3264,
     9396, -6622, 866, 9454, 4568, -6283, -9395, 5571, 1852, 4225, -2240, -4085, -1947, 6282, -402, -3668, 2856, -3157,
     -1207, -821, -9157, -9706, -3059, -7766, 8096, -4785, -8032, 9549, -246, 2107, -9114, 4969, 8656, -4198, 8862,
     4998, 1333, 754, -8272, 8053, -5895, -6466, -8942, 9123, 480, -7590, -7003, 7635, -2787, 3306, -1426, 3121, 5481,
     -1988, 6581, 1961, 2840, -1485, 8741, -7160, -5012, 5988, 3385, 4146, 7236, -7857, -213, 1522, 6533, 5625, -1393,
     -7745, 2114, -6554, 5327, -1923, 3620, -475, 7214, -6366, -647, -7150, 8124, 4773, 1379, -2331, 6569, 712, 5142,
     8172, 1909, -1775, 6846, 4834, 2139, 2862, 1674, 124, -2143, -6352, 9527, 1032, -2364, 7452, 9555, -6917, 8727,
     -5303, 1016, 9418, 9009, -4900, -3717, -8094, 9308, -3734, 6889, -9020, -7255, 9136, -6502, 4754, 8007, -3553,
     6621, -9887, 7165, -5888, 4871, -5054, 4551, 9497, -8242, -1074, 9346, -6785, 658, 2940, -3551, -7351, 4970, 9875,
     -549, -2678, 1895, -8681, 8113, 3513, 3814, -603, -1681, -9169, -8353, 8399, -3327, 2397, -5185, 6570, 4196, -5021,
     4547, 7128, -8991, 2630, -3355, -6151, 2491, -9736, -1390, -1180, -2960, -5116, 3485, 5002, 901, -7386, 8790,
     -1962, 190, 3097, -6429, 2815, -8061, -3195, 2311, 100, -9665, -5786, -6537, -8466, 3266, 543, 1628, -5824, 1160,
     -5396, 7511, 1835, 2279, -114, -5036, -8406, 9729, -2730, -5432, -5807, 7778, 2738, -1692, 2371, -1217, -6721,
     -9377, 8162, -8638, -5375, 8145, 8178, -3356, 6293, -4336, -7357, 7368, -6077, -2523, 7213, 2478, -6353, 1667,
     5499, 357, -222, -6212, 3039, -8204, 2395, -6318, 6422, 6418, -8972, 611, 7211, -7928, -4997, 7603, -375, 9557,
     1481, -5260, -8262, -5448, 1860, 9245, 6486, 2144, 6654, 8272, -2350, 8233, -6425, 7723, 777, -9881, -5674, -1631,
     8677, -5850, -3087, 9476, 9018, -9287, 9939, -9243, 9752, -4692, -723, -7967, -1476, -1192, 9830, -9362, 8883, 522,
     -8042, -3363, 7444, -3914, -244, 8514, -6967, -7156, -7691, 5822, 9825, -8379, -8097, -8587, 7845, -1247, -2819,
     -1971, 3106, 9591, 8243, -3183, -1297, 436, -613, -4664, 3275, -1722, 3780, -4515, 5889, 3360, -1977, 7641, -9092,
     -9161, 4922, 5750, -5686, 7325, 7172, 7188, 2088, -9067, -9069, 9799, 3221, -6016, 9128, 3584, 6567, 2346, 8128,
     -9925, -3000, -5769, -6021, -6952, -4603, -9296, 6489, -1540, 3740, -5348, 7338, -1677, 9075, 8051, 6663, 4583,
     -1560, 839, 8210, 202, -662, -5267, -1508, 3540, 3619, 3932, 4548, 9253, 9637, -5090, -5944, -8771, 119, 6086,
     -2995, 752, 9013, 2953, -5557, -4612, 6675, 5041, -6322, 2398, -492, -3432, -761, -3458, -5011, -7087, 7520, -2209,
     -7542, 1658, -325, -2429, -4022, 74, -9715, 2552, 1947, 225, -8295, 5667, -6076, -7314, -8977, -1283, -1980, -4481,
     -2201, 8209, -1764, 4573, -7808, 5180, -1777, 3166, 5806, 7209, -8236, -6035, 6856, -3128, 3948, -621, -3809,
     -2982, 1375, 7797, 4703, 7110, -1017, 59, 4900, 934, -922, 994, 6525, 6501, 2339, 6873, -129, 7594, -1638, -9183,
     3951, -3346, -1835, -6885, 8763, -2890, 4528, -7086, -7628, 674, -1559, 4207, 8636, -4690, 8623, 9508, -4938, 1200,
     -4577, 9367, -477, 7040, 332, 8406, 7961, -2565, -2354, -6669, -4539, 9601, -5234, 228, 8594, -6860, -9791, -2421,
     7474, 5469, 8668, 7824, -1097, -1706, -1463, 2974, 5177, -3969, -8323, 812, -5971, -4985, -3718, -4129, -8347,
     7010, 5698, 457, -5057, 7897, 8286, -2831, 4228, 596, -5468, 3046, 9273, 8415, -1882, -780, -98, 5602, 5749, -5788,
     2656, -8492, -8394, 6634, 8417, 3734, -1903, 7248, -519, -5568, 2545, 8859, 2504, 6290, 1660, -3557, 150, -309,
     -6368, 4431, 1165, 3391, 2127, 8031, 7378, -9922, -5853, -57, 542, 9227, 7591, 7196, -2704, 6468, -6914, 4073,
     5595, -3700, 7226, 7182, 3204, 809, -7497, 9755, -8970, -5477, 1988, -9211, -1511, -1062, 1949, -7851, 219, -473,
     -1227, 5428, 2604, 1151, 4181, 1311, -9044, -5255, -4966, 9299, -544, 3155, 8315, 9055, 3539, 7388, 5090, 8306,
     -3007, 6095, -7401, -9692, 4504, -9939, 4806, 8132, 5079, -652, 7348, -5793, 3322, 6382, 2307, -510, 8203, 2055,
     -1829, 4135, -3159, 9616, -3538, 3831, 5726, -5795, 8080, -9708, -5711, 8467, -7158, 6906, 1900, -6248, 775, 6598,
     -4598, -223, -9909, 8262, -7530, 394, -6971, -24, -645, -397, -5719, 8707, 7291, 6429, 4709, 5630, 6768, -8663,
     8642, -3310, -1983, -7944, 9964, -7575, 8795, -2529, 9653, -6987, -8961, -197, -1702, 8049, -5746, -608, -9770,
     5676, -6696, 189, -2711, 6745, -3369, -3810, 5868, -8277, -7952, 626, -1430, -3509, 3488, -8656, -5122, 7075, 993,
     9723, 2289, -8083, -9210, -7122, -5401, 8797, -9907, 5518, 6113, -6570, 1889, 493, -6660, 2035, 7579, -466, 3134,
     8986, -3247, -1030, -5943, 400, 1438, 7588, -4189, -6130, 8621, -9468, 311, -6858, -5649, 1068, -8510, -7100, -584,
     6244, -8781, -1261, 3868, -377, 8246, 6078, -8744, 950, 7323, -3103, 3196, -5528, -3263, -9131, 7813, -7330, 5556,
     303, 2186, 9606, 4572, -2262, -7085, 7032, 7111, -6397, 4668, -9397, 2294, -9493, -8364, -7706, -7709, 4168, 9379,
     4211, -8386, -6412, -4816, -3837, -3708, 1652, 379, 3653, 4975, -2142, 3065, 1362, 6763, 9619, -4068, -8965, 6879,
     -5581, -5321, -8542, 8715, -904, -7841, 3130, -9837, 3194, -2466, -6277, 347, 8861, -7018, 8332, 6523, 3708, -2630,
     -3745, -5696, -2317, 6392, -947, 37, -4988, 2217, -5816, -6229, -5365, 3092, -374, 4560, -9258, 1085, -4122, 5030,
     -8612, 7955, -1472, 2542, 2048, -2391, 3986, 8510, 9570, -1697, 3161, 744, 857, -4502, -7194, 5023, 6069, 1582,
     1197, -2651, 2117, -5552, 9809, 292, 617, 9918, -7409, 8469, -3420, 1127, 846, -7994, -3873, 5550, 569, 1761, 2378,
     -501, 3333, -7064, 2966, -8404, 2040, 6642, -2528, 1536, -7019, -2611, -6446, -3777, -1343, 8063, -1854, 7798,
     -875, 2737, 6187, 2475, 4443, 372, -3953, 5058, 5357, 2006, 3223, 9884, -5638, -5775, -966, -8441, -8809, -6935,
     3517, -2260, -4365, 2963, -8210, -7874, 5998, 404, 159, -6661, -1760, -8357, 9611, -6069, 9843, -1996, -3419, 2896,
     4042, 254, -1411, 8353, 4971, 7703, 3439, -7879, -7124, -6098, -6309, 975, 3312, -7177, -8932, 8143, -6402, 6140,
     -128, 3812, -3922, 7544, -2747, 4543, -7946, 4193, 4176, -3910, -8184, -529, 1665, 3842, 383, 8119, -5986, -4058,
     -6950, -4454, 8346, 2821, 2406, 5223, -2810, 7416, 4564, 6796, -3911, -1134, -7815, 2308, 2667, -1759, -6319,
     -2434, 8997, 9184, 6786, 3279, 5902, 4085, -2689, 1809, 4643, -8294, 9324, -5115, 7552, -6100, 3749, -9864, -4881,
     -1530, 6733, -2408, -2570, -8179, 6184, -3792, 3172, 2605, -4276, -1262, 9231, 2946, -1038, 3051, -8992, 9042,
     4555, -1091, -5511, -4948, 9987, 4328, 2147, 689, -7114, -7082, -1685, 1997, 5672, -7783, -869, 3783, -8730, -3328,
     5644, 4238, -7389, 973, -9337, 7593, -61, -7438, 3953, 3429, -5310, -384, -8499, 7140, 5780, -4109, 9442, 9370,
     -9098, -1354, 9760, -2222, -7365, -575, 2964, 3805, 9431, 6412, -6362, -7685, -3578, 7494, -8829, 7340, -2888,
     8249, 3650, -876, -6886, -9093, -7708, 2980, -9341, -9191, -4240, 5246, 7820, 7697, -4991, 1593, 7769, 7339, -4232,
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     -2326, -395, -7191, -1902, -3669, -8926, 7585, -2791, -3999, 2565, 7091, 270, -3298, -3849, -7094, 9775, 9969,
     7551, 5588, 4355, 5298, -2663, 2043, 4952, 2452, -3422, 7317, -7475, -3862, -7583, -2602, -2428, -6538, -2657,
     5452, -205, -4202, 6956, 1725, -1975, -261, 1505, -342, -4222, -2014, -8460, 5194, 5761, -4283, 9647, 7041, -2892,
     -5680, -3920, -3049, 3983, -764, 3537, 7643, 7266, -2620, 9363, 6993, 8708, -4004, 1009, -4901, -7999, -7448, 68,
     7181, 4472, 1452, 8683, 6090, 8116, 1161, -3316, -5130, -7921, -4540, -3902, 882, 3993, -5965, -1400, -6813, -1046,
     4765, -3287, -2109, 9887, -3727, 4155, -311, -7264, -6752, -2432, -7320, -7814, 2677, 1188, -1423, -1447, -8667,
     -6790, -7029, -8234, 2888, 3442, 130, -6845, 3883, -5631, 8273, -4209, 1378, -3619, 4130, -2849, 6599, 8484, 8802,
     -4469, 5927, 1687, -7596, -2279, 5063, 6835, 1408, -6539, -6165, 5819, 6661, -532, -9702, 3634, -5149, -8286, 369,
     -602, -3306, -1691, -9452, 929, -6903, 1301, 4394, -3052, 6917, 3170, -1955, 7852, -3214, -7617, 8730, -7581,
     -9627, -8907, 6898, 6309, -7170, 2742, 5915, 7922, -2733, -1372, -5620, 1390, -5339, 9770, 3295, 7787, -3892,
     -3408, -6675, 7290, 6625, 781, 3228, -6259, 9524, 7879, 1090, 6147, 4603, -5817, -9271, -7612, -6102, 8068, 1033,
     -6257, 3640, -5294, -711, 4449, 2998, 1977, 1054, -5088, 1149, 4731, -3746, -6207, 6557, -7089, -2569, 962, -2548,
     -8888, 8618, -367, 9012, 515, -2859, -3610, 4590, 8684, 2375, 7620, 5018, -4072, 2347, -3713, 6961, 7123, -2513,
     -1363, 2465, -5595, 6971, -568, 9779, -7188, 8845, -1253, 2131, -3216, -7642, -7065, 6814, -6872, 4875, 7705,
     -7442, -9430, -4151, -6672, 5473, -5109, 6068, 2503, 9670, 167, 8539, 8834, -836, 9015, -5586, -8180, 4056, 9520,
     -8872, -8849, 9552, -3472, 6679, 5389, -9839, -9010, -8458, -8954, 5069, 7500, -3937, 5954, -3051, -7843, 2281,
     -8171, 5929, 377, 7645, 6936, -3116, -6231, -9340, 3595, 2410, 6706, 4327, -2793, 9221, 1656, 714, -8201, 5919,
     -6037, -2872, 4734, 6645, 7542, 7107, -880, 8223, 1516, -4645, -9741, -4835, 1156, 2680, -3037, 1571, 1485, 2324,
     -5363, 8807, -9460, 1684, -2757, 8731, -3971, 2392, 2578, 2320, -1841, 4169, -8988, -5642, 489, 7627, 6871, 8995,
     -280, 6323, 2137, -7972, -585, -9995, 5438, 1643, 8435, 2519, -9779, -5702, 8501, 6026, 2502, 4039, 9361, -171,
     1340, 4428, 5648, 3087, 7677, -9965, 5502, 3190, 8319, -7592, -9365, -5323, -9348, 7766, 7653, 7383, 3147, 8354,
     2724, -663, 4322, 2154, -3555, -4967, 3202, -8002, 8110, 3083, 1651, -6075, -6739, -8405, -4039, 1816, 5894, 3010,
     7957, -8190, -7896, -1866, 9598, 80, 2777, 3646, 3043, 2240, -412, -958, -2836, 561, -7638, 2255, 7549, -1620,
     -1361, 2202, -1012, -7334, 4268, -7763, 5150, 3074, 5100, -9642, 6714, -2170, -2191, -6436, -658, 7332, 7878, 1163,
     -6606, -551, -441, 8411, 9867, -1453, -4983, -6380, -3398, 497, 6472, -5163, 7819, -1127, -3377, -6218, -8560,
     -773, -2807, -9927, 5649, -7030, 1400, -6440, 1576, 2570, 8208, 3474, -3670, -2405, -4086, -523, 6181, -2504,
     -2018, 1975, -2048, -6194, 5042, 2922, 9642, 9714, 7622, -6346, 3688, 2065, 5912, -1749, -2335, -4959, 1464, 8523,
     3167, -3453, 4764, -545, 9386, 4917, -2750, -2056, 9565, 9177, 4509, 685, -6645, -866, 8468, 4544, -3281, 7235,
     484, -4471, -6184, -6928, -8036, -9516, 3806, 1100, 2615, 6164, 2044, -559, -2083, 5370, -1034, -2379, -8576, 8674,
     -5843, 616, 6488, 7071, 5579, 3303, -6361, 1330, -4812, 2655, -8158, -6020, 8649, 9039, -2065, 9427, 1420, -5690,
     3711, -7476, -8416, -4639, -9573, -7067, 9561, -1665, -8580, 289, 3541, 3618, 7469, 9906, -5783, -1025, 5415, 6085,
     9, 1827, 9885, 6146, 583, -8014, 8632, 9746, 433, -6347, 9587, -636, 2017, -4677, -4592, 140, 2844, -8503, 4010,
     -562, 9608, -1519, 1633, 7905, 9818, 9191, 2352, -6823, 8934, 5650, 3452, -8279, 5003, 388, -7604, 1521, -207,
     2317, -5024, 1351, -950, -9771, 5626, -4121, -8273, 151, -4526, -4725, -5881, -921, -7339, -121, -3297, -7256,
     -8651, 1137, -811, -912, -7013, -2557, -4763, -8099, 6767, 5969, 8221, 3424, -5161, 5463, -4308, -3934, -3612,
     8528, -6530, -3650, 2670, -1813, -9315, -9089, 8042, 2096, 264, -1408, 8630, 6788, -5761, -137, -1970, -1230, 8728,
     7310, -2127, -107, -7119, 5204, 41, -3846, -9662, 4371, 983, 2797, -5700, 9393, -2748, 8030, -9238, 4439, -89,
     -7474, -4503, -5265, 1144, -5164, -5799, -6344, -6725, 9648, -9060, 893, -5152, -8989, -9782, 3937, 553, -1796,
     -2202, 7505, -4908, -4759, 4082, -767, 9209, 7193, -2229, 2066, -6369, 4102, -6070, -5836, 9343, -7660, 6666,
     -4940, 3239, 1482, 110, 3291, -573, -8443, -4194, 3367, -6712, -6884, 8905, -9456, 7678, -1546, 6128, 2961, 2259,
     -4744, -6129, -1342, -5539, 8485, -6000, -8968, -7313, -5737, 9072, -1541, 5365, 2919, -6519, -6308, -4742, -8420,
     4334, -1705, -8665, -6378, 4690, -8664, -7933, 607, 3810, -6416, 2968, -7263, -730, -6258, -1404, 1295, 3532, 886,
     -7910, -7989, 9120, 7133, 6881, -7411, 1496, 2506, 15, -8619, -1289, -8512, -739, 1106, 5012, -6924, -8410, -7936,
     3119, -4152, -3716, 6968, -9137, -4644, -5530, -8632, 9056, -9938, 8719, 6659, 6791, -5106, -1149, 9220, -6083,
     -3164, -4111, -1333, 981, -7073, 9266, 8073, -3804, 8107, 4772, 7493, 1605, -7870, 5847, -995, 2366, -8390, 872,
     5244, 588, 4143, -1016, 4359, -7084, 4417, -5093, -6514, 2309, -458, 3767, -1132, 4026, 1363, -1270, -1435, 1024,
     -601, 6509, -6441, -9518, 4393, -5744, -6249, -7601, 8205, 9963, -8558, 1920, 9228, -2967, -7063, -8239, 3969,
     -3534, 9664, 3815, -8480, -2621, -4833, -8222, 1056, -7791, -1095, -9042, 8206, -3234, 8838, 5187, -389, 2249,
     3025, -4846, -4913, -7767, 7478, -1436, -8064, 3632, 9950, -1780, -7426, 5776, 4990, 5496, 88, 4202, 794, 9515,
     -3124, 7005, -1441, 7850, -210, 6977, -9206, -7510, -9424, 4064, -6664, 3215, 4029, -6153, -9668, 889, 9573, 5490,
     -2341, 4865, -7657, -2897, 2205, 1554, -7445, 8611, -9076, -1315, -4708, 7789, 7066, -9257, -8628, -849, -230,
     -8209, -8133, 2810, 632, 2402, 4776, -9135, -7522, 4742, -6080, -4075, 3699, -6005, 913, -3989, 1237, -4285, -3360,
     -8418, -5478, 9407, -1194, 3492, -6587, -5499, -987, 149, -2581, 2789, -347, 2661, -6009, 8438, -637, 4464, -3376,
     428, 2109, -7707, 6080, 3930, -3696, 3906, 1804, -4009, 7372, 3716, 4367, 641, 1710, -9548, 3253, 3066, 450, -9475,
     -1416, -7385, 4263, 1189, -2846, 3455, 127, 9528, -4262, 4395, -5886, -8957, -1875, 3574, -7106, 2164, -3845,
     -5476, 5364, 7282, 2112, -6170, -7130, -3163, -117, -6290, -4435, 7227, 3754, 1069, -6121, -6281, 9385, -9953,
     4718, 5580, 2222, 2302, 8090, 9160, 9076, 6959, -7239, 4075, -390, 2908, -2430, 4108, 8774, 9681, 8792, 6424,
     -3358, 5852, -2662, 7246, 5810, 8445, -6356, -5137, 843, -6506, -6581, 1690, -994, -1218, -4643, -816, -2596,
     -3149, -6480, 8635, -8790, -5463, 7409, 6192, -956, 2887, -8533, 1696, -7337, -7506, 2337, -7845, 6537, 9444,
     -6896, 863, 1129, -1181, -2717, 7070, 6079, -4683, -6985, 5050, -7938, 3549, 614, 5846, -5991, 2692, 8658, 3817,
     -9162, 6158, -5992, 5574, 2036, 7927, -2763, -5495, -1613, 1044, -7749, 7103, -3769, -6915, 6547, 2596, -3133,
     -9073, 3534, -4224, -9242, 4107, -6012, -9912, -6822, 8432, 6286, -6023, -1900, -1863, 1328, 2914, 1693, 7, -9050,
     8356, -612, 2090, 5562, 7015, 8702, 4374, 9196, -8620, -4588, -2877, 3505, -6345, 1574, -1767, 7311, 2451, 8392,
     -8938, -1671, 7408, 386, -9777, -7113, 6813, 3576, 446, -5849, -9545, 3177, -4351, 4536, -2306, -1956, -5016, 8441,
     -9749, -8931, 8405, -5694, -7828, -4002, -7446, 9436, 8800, -9560, -3857, 4282, 7772, -9416, 8229, 8695, 3241,
     -8354, -936, 936, -3293, -7897, -6302, 6568, 8097, -1031, 5936, 6039, 7468, -8960, -3582, -6595, 8596, -257, -4825,
     1664, 3700, 6527, -5082, 9179, -4238, -5810, 6587, 2928, 7428, -7620, -145, -8647, -1100, 1606, -2474, 3897, -8015,
     -2769, -3781, 1466, -5447, -7552, 6127, -5107, 4138, 1093, 1954, -5599, 5309, 7122, 8470, -620, 8568, -4717, -2705,
     -5864, -8549, 7195, 8414, 941, 7728, 5084, -8516, -9496, -8018, 9044, -2139, -4804, 3692, 3244, 3363, 126, -139,
     7146, 4031, 1887, 7977, 8498, 2242, 9934, -3318, -9431, 2590, 9568, 8798, 1564, 5598, 6380, -44, 6588, 6091, 8646,
     6674, -9415, -2845, 6945, 2199, 7117, 3575, -547, 1999, -5665, -928, -1454, -6601, 7805, -1501, 2702, -7243, -9968,
     419, -2944, 5440, -1330, -7902, 2447, 5341, -4286, -1088, 2893, -5289, 5259, 507, -9117, 4066, -6814, -7068, -5884,
     5038, -8575, -9876, -3528, -3203, 9719, -9056, -7072, -3455, -5969, -7970, -5713, 5489, 5841, -7379, 8691, -4099,
     8662, 8082, 9635, 3338, -7217, -8156, -4253, -64, -703, -8400, 3382, 2256, -8302, -8891, 9506, -5155, 4246, 3617,
     8355, -815, -2929, -1853, 9761, 4850, -8448, -1493, -9747, -2074, -8251, 2707, -9506, 6370, -2615, 380, -7723,
     4052, 7708, 5728, -5835, -9387, 9595, -3694, -4297, -2207, 3197, 2367, -2488, -8676, -3503, 6847, -3554, -1386,
     9960, -4903, -3719, 6285, -9697, 7391, -9727, 3622, 4523, -1958, -772, 504, -5305, -1455, -1061, -824, -2841,
     -6687, -5442, -5370, 5172, -9644, -184, -777, 9147, 622, -2925, -1816, 7440, 3878, 9738, 137, -2348, -9826, -7696,
     -4672, 6467, 2883, 953, -5098, -3269, -5566, -2107, 1122, -5662, -1670, 9580, -4670, -5947, 405, 2923, 3036, -1085,
     7801, 7971, -615, 3296, -5768, -9767, 3694, 5858, 398, -2698, 5739, -1937, 1302, -9177, -1811, -9558, 4295, -3618,
     -5089, -2246, -4266, -7751, 5098, -8806, 9985, 3702, -9701, 7369, -8836, 1941, -7433, 5802, -9526, -1043, -6776,
     -5601, -9048, 3324, -435, 6648, 5479, -2336, -8980, 5882, -8511, 3931, 2585, -4916, 7621, -1845, -1015, -9489,
     3518, 9453, -9946, 4595, 4468, -9277, -1984, 5906, -9017, -9171, -1990, 9043, -5299, 4921, 1288, -6981, -3735,
     5614, 5458, -3941, -1961, -6211, 5509, -560, 1777, 3026, 604, -2471, -3462, -9624, 9276, 8425, -2686, -5091, -8267,
     4841, -2403, 2393, 3543, 2697, 6807, -1009, -9265, -3711, -8450, 5798, -4003, 1219, 9961, -7008, 8487, -4802, -881,
     6338, -3948, -385, -3142, -1506, -4930, 577, 3893, -8135, 9278, 3960, -6643, -8055, 4869, -7297, 703, 696, -6676,
     7077, 6837, 8799, -4832, 3874, 4899, 2299, 8908, 3258, 5910, 7497, -5841, 4159, -299, -2538, -9799, -3654, -1265,
     -8761, 1371, 1017, -9674, -4071, -9765, 1059, -768, 5695, -507, 3959, -9731, 3750, -2506, 6420, -1516, 6295, -1104,
     6225, -7250, -1477, -1734, -9244, -2019, -3903, 4406, 4308, 1603, 6124, 7394, -7190, -889, -3803, -5332, -9051,
     680, -6589, -1496, -9885, -8606, 9769, 1092, -8921, 765, -100, 5624, -1070, -4197, 9849, 824, -990, 3116, 979,
     -8297, -2739, -9478, 9631, 1395, -1590, 9510, -8787, -1352, -5482, 5483, -1412, 6740, 4427, -7812, 2808, 9827,
     7919, 977, 532, 8239, -704, 8384, 2277, 7851, 4789, -3997, -9359, 2532, -8933, -635, 4264, -7849, 4276, 1883, 1785,
     -5033, -1290, 138, -8276, 6067, 4513, -4105, -5331, -7148, 4561, -2173, 4254, 9353, -1498, -8311, 2487, -505,
     -8827, 5056, 5073, 1948, 9071, 2727, -238, -6101, 5387, -218, 2593, -4342, 3399, -5395, 6180, -6107, -8944, 8212,
     6246, -8655, -1718, -8185, 798, -7895, 334, 4616, 6448, -321, 5251, 7782, -1712, 1859, 1778, -7238, 7883, -4806,
     -8183, 5901, 5510, -9710, -4295, 5249, 9584, 4575, 4829, 7567, 6500, 2495, 274, 7446, -1746, -3392, 3913, -8680,
     -633, -7001, -9934, -6583, -178, -7687, -4098, 3835, 1931, 2045, -2561, 5095, 2693, 7608, 7343, -2694, 9206, 4933,
     -4978, 4484, -3350, -9088, -7168, -7096, -289, -456, 8552, -9385, 6695, -4346, 4795, -4057, 1604, -8268, 9364,
     2663, -1029, -9742, 9626, 7321, -6279, -4047, 679, -2040, 8216, 7153, -1248, 71, 6759, -3571, 663, -8034, -2274,
     -5757, -9975, -7300, 7023, -8479, 2715, -2473, 220, 1456, 6213, 470, 4567, -8065, -6557, -9369, 9232, -6299, 868,
     -6215, 8928, 9816, -3687, 5516, -1130, 2443, -1349, 2749, 3449, 3729, 3762, 146, -9935, 6736, 2198, 5669, 9087,
     2305, 9882, 3747, -1260, -3409, 7861, 5965, 2536, -8724, 722, 173, 4053, -4771, 136, 3470, 3184, -9332, -8745,
     3227, -7630, 7749, 2113, -6970, 3446, -9745, 4407, -570, -6635, 5035, -2445, 2843, -2775, 802, 6307, 1510, 9997,
     -1578, 5953, 296, -2614, 9399, 9004, -8128, -3315, 5125, 1470, 3662, 6584, -3676, -1150, -8573, 4481, 6191, -3317,
     7976, 4170, 9114, -1992, -4201, -9552, -9567, 9955, 3150, 4700, -3709, 2011, -3939, -8010, 5431, 5951, 5564, 1459,
     -6112, 375, -2790, 7443, -4018, 3251, -9932, -2912, -2713, 9414, 924, 8735, -5646, -5936, -3838, -8001, 3755, 6722,
     -8798, 4132, -7469, -6063, -9988, 4958, -7081, -1600, 5064, 6790, -7015, 4740, -5548, -4890, -9788, 9676, -9533,
     -9216, 1548, 9335, -5580, 9285, 8431, 1014, 618, -3608, -9327, -1786, 2130, 8171, 2435, 435, 55, -3342, 5514,
     -7332, 8488, 2973, -2608, 1296, -1391, 6117, 1425, -1716, 4905, -5974, 8951, 7294, -5356, 3724, -5415, 8639, 2800,
     376, 2571, -1868, 9003, 8765, 9305, 6978, -5691, 9455, 8454, 8991, -2256, -6027, 62, 2860, 4069, 1300, 1540, 7533,
     3487, 6830, -2691, -9109, 3798, -6895, -7285, -3543, 7963, -6420, -1768, 9612, 7786, -5178, -9316, 8736, 1240,
     -2345, -1212, 540, -4388, -1156, 3113, -3359, 6022, -1994, -2154, 771, 9052, 4197, 8536, 9495, 3062, -2522, -2672,
     7874, -9342, -5050, -4207, -4249, 4289, 636, -4378, 7191, 3923, -6175, 7215, 4447, -7578, 7662, 6326, -5195, 1421,
     -6071, -1457, 5718, 9287, -7374, -9851, -2873, -4247, 4973, -8521, -7031, -7491, -3788, -3354, 9405, -3220, -8598,
     4147, -6621, -7390, 4152, 4845, -9386, -2055, 2399, 3939, 5111, 9576, 8473, 6446, -1550, 9541, 7288, -8012, 2104,
     -7809, -8650, -6389, 1081, 2120, 235, 7914, 8693, 8610, -2721, -4705, -1898, -4042, -9001, 458, 7568, -4912, -9143,
     -4083, 2295, 4492, 5996, 4870, -3884, 5215, -1335, 6984, -5407, -5266, 1986, -2720, 2525, 7277, -6723, 2013, 7061,
     6925, 6513, -932, -2030, -6185, 589, -6966, -215, 8141, 3668, 3580, 1862, -3653, -6780, 502, 1663, 2863, -4638,
     2118, 7715, 9650, 8718, -8387, -2803, -3986, 4934, 1770, -9504, -810, -3793, -4596, -2789, 7299, -8964, 5877, -537,
     -5302, -6467, 7354, 8548, 1463, -6317, -7449, -229, -1877, 5711, 4239, -1973, -6610, -1897, -8914, -2131, -365,
     -8707, 1794, 3623, -4527, -343, -8163, -2068, 8393, -2588, -5087, -4986, -1565, -7454, -7216, -7187, 1267, -5171,
     8163, 640, 4562, 8, 6665, -7149, 8122, -7304, -841, -90, -5127, -7262, 9896, 1611, -590, -2325, -7172, 2526, 2770,
     9921, 9272, -9628, -9997, -9778, 5425, -7532, -2692, 7142, 2215, 3985, -6816, 7606, 6876, 211, -9583], 10000, 0)

print(datetime.datetime.now() - startTime)